I would prefer the answers typed out but if you MUST use paper be clear and neat. Answer each question correctly and briefly explain how you got the answer. Use your knowledge of Lines and Planes specifically for this! Thanks!

1) a) Determine the symmetric equations for the line throughP(5, 6, 10)and parallel to the line with equation= (6, 1, 1)+ t(2, 1, 3).

b) Determine two other points on this line

2) Find the value ofkso that the lines and are perpendicular.

3) Determine parametric equations for the plane through pointsA(2, 1, 1), B(0, 1, 3), andC(1, 3, 2).

4) Determine a vector equation for the plane that is parallel to thexy-plane and passes through the point(4, 1, 3).

5) Determine a scalar equation for the plane through the pointsM(1, 2, 3)andN(3 ,2, -1)that is perpendicular to the plane with equation3x + 2y + 6z + 1 = 0.

6) Show that the line with parametric equationsx = 6 + 8t, y = 5 + t, z = 2 + 3tdoes not intersect the plane with equation2x y 5z 2 = 0.

7) Determine the intersection, if any, of the planes with equationsx + y - z + 12 =0and2x + 4y - 3z + 8 = 0.

8) Solve the following system of equations and give a geometrical interpretation of the result.

a) x + y + z = 6

b) 2x + y 3z = -5

c) 4x 5y + z = 3

9) Give a geometrical interpretation of the intersection of the planes with equations

1. x + y 3 = 0
2. y + z + 5 = 0
3. x + z + 2 = 0

10) Determine a scalar equation for the plane that passes through the point(2, 0, 1)and is perpendicular to the line of intersection of the planes

2x + y - z + 5 = 0andx + y + 2z + 7 = 0.

11) Explain why there are many different vector and parametric equations for a line